"Ouch, I'm going, I'm broken!"

Doing math problems is the same as writing a novel, the thinking is smooth and ten changes a day, and if the thinking is broken, one change is one change every ten days.

At the critical moment when Shen Qi was about to solve the first geometry problem, he was interrupted by the vice president.

"This uncle is really annoying. Shen Qi had to reorganize his thoughts, which took him an extra five minutes.

The verification process filled the entire blank paper, and Shen Qi finally found the value of sinψ.

To his surprise, sinψ was actually 1/2, which is a 30-degree angle.

Take a ruler and measure it, it seems to be 30 degrees.

Using Lobachevsky's drawing method, it turned out to be 30 degrees.

"I'm stupid, I'm really stupid......" Shen Qi realized a low-level mistake, he was confused by the complex geometric pattern, and it took nearly 1 hour to derive it forward.

If you first use Lobachevsky's drawing method to directly calculate the degree of the ψ, and then reverse verify that the ψ angle is 30 degrees, you can save at least half the time.

Of course, Lobachevsky's drawing method certainly cannot be drawn on an exam paper, and it is no problem to draw on scratch paper.

It is easier to verify a conclusion with a conclusion than to deduce an unknown.

It's a game, a math game between the questioner and the answerer.

Fighting a war is the best training, and exams are the best review.

Although there is systematic assistance, Shen Qi also has a new understanding of mathematics in the extremely difficult semi-finals.

There must be a deeper relationship between the hypothesis and the proof, and the truth or the fallacy is not as simple and antithetical as it seems, and the fallacy may be a reversal of the truth.

Shen Qi was distracted, he thought a lot, he thought for a few minutes, it seems that his math level is still too low, and he can't understand many questions.

"There are still two hours left in the exam, so please hurry up and answer the questions. An invigilator said to all the contestants.

"Two hours, two questions left. Shen Qi came back to his senses and moved on to the next question.

This semi-final exam paper is the least number of questions he has ever done, with only three questions.

At the same time, it is also the most difficult one, and the first question with the lowest score took Shen Qi 1 hour.

The second problem is an algebra problem that looks like this:

1

1-1

1-2-1

1-3-3-1

1-4-6-4-1

1-5-10-10-5-1

1. Please calculate the sum of all the numbers in line 1024. (five minutes)

2. and prove that any number in line 4201 is a fraction or a negative number. (15 minutes)

In fact, many high school students know this number triangle, who doesn't know Yang Hui Triangle, middle school students who have participated in the number federation and Olympiad competitions know the regularity of Yang Hui Triangle.

Of course, Shen Qi understands this number triangle, which is called Yang Hui triangle in China and "Pascal triangle" in the West, named after two Chinese and Western mathematicians.

The regularity of the Yang Hui triangle is not difficult to observe, and each number in the triangle is the sum of the two numbers immediately above it.

And so on, Shen Qi quickly calculated that the sum of all the numbers in line 1024 is xxxxx... This is an astronomical number, expressed in 2 to the power of 1023.

The first sub-question of the second question is simply a score question, so the score is not high, only 5 points.

The second question is difficult, with a score of 15 points.

Positive derivation of any number in line 4201 is a fraction or a negative number applies, which is a headache, and I can't find a clue at all.

If Shen Qi wants to reverse the extrapolation, the content of the proof required in question 2 must be able to find a formula, theorem or inference as the basis.

"Bernoulli's permutations or probability theory? No, not really. ”

"Neither are the three special types of equation expansions of Veda. ”

"Playing this pure numbers game, Fermat is a top master, yes, it should be Fermat, he and Pascal are good friends, the two often exchange letters, and this question is based on Pascal's triangle. ”

"Fermat put forward hundreds of hypotheses in his life, and 99% of the hypotheses were proved to be true, he is known as the 'king of amateur mathematics', but I never believe that Fermat's level of mathematics is the same as mine. ”

"Big head, I've only studied 70 of Fermat's 273 hypotheses at most, which one is it?

Shen Qi put down the ballpoint pen, closed his eyes and recuperated, racking his brains to find a way.

The vice president swayed behind Shen Qi again, he showed a smug smile, and was very satisfied with Shen Qi's current state: "Young man, even if you can solve the first geometry problem and be familiar with the laws of Yang Hui's triangle, then what can you do?

At this moment, Shen Qi suddenly opened his eyes, and his eyes were bright: "I thought of it, this is Fermat's (1+a) inference!" He said that this inference must be valid and does not need to be proved, but 100 years after his death, his French compatriots proved this inference. ”

The idea is coming, the idea is coming!

Shen Qi's inspiration gushed out like a spring, and he picked up a ballpoint pen and prepared to solve the problem.

Just as he was about to start writing, Shen Qi inexplicably felt a chill behind him, the same as just now.

Shen Qi glanced back, very unhappy: ", it's you again!

The vice president pretended to be calm: "The examination room is so big, as an invigilator, I occasionally pass by." After saying that, he left with his hands in his hands.

"Uncle, you're really annoying!" Shen Qi calmed himself down as quickly as he could, and entered the proof process of the second question and the second sub-question.

Ten minutes later, Shen Qi wrote out the entire proof process of the second sub-question, and the proof was completely valid, and any number in line 4201 is a fraction or a negative number.

"The first and second questions have been solved, and 35 points have been obtained. ”

Shen Qi, who had broken two questions in a row, was greatly boosted, and he began to do the last question.

The vice president was an idle man, and after a lap, he detoured behind the other competitors to observe secretly.

"He Tao, this young man can't do it, except for knowing Yang Hui's triangle, he can't write any other questions at all. ”

"Luo Ming, from Nangang City Foreign Chinese School, after all, it is a student of a famous school, this young man is okay, the first geometry question is answered correctly, but the second question of the second question is obviously wrong, young man, you are in the opposite direction." ”

……

The vice president visually inspected the player with the fastest and highest accuracy in the whole examination room to answer the questions, and he couldn't help it, he couldn't help it, so he touched Shen Qi's back again and observed secretly.

Shen Qi suddenly turned around, he was about to collapse: "Uncle, don't do this, why do you have to get along with me?"

The vice president is still very innocent: "I issued this exam paper, I'll take a look, can't I not speak?"

"Damn, did you come out of this volume?" Shen Qi never expected that the master of the question in his mind was actually this obscene uncle.